### Distance antimagic labelings of product graphs

#### Abstract

*G*is distance antimagic if there is a bijection

*f*:

*V*(

*G*)→{1, 2, …, |

*V*(

*G*)|} such that for every pair of distinct vertices

*x*and

*y*applies

*w*(

*x*)≠

*w*(

*y*), where

*w*(

*x*)=Σ

_{z ∈ N(x)}

*f*(

*z*) and

*N*(

*x*) is the neighbourhood of

*x*, i.e., the set of all vertices adjacent to

*x*. It was conjectured that a graph is distance antimagic if and only if each vertex in the graph has a distinct neighbourhood. In this paper, we study the truth of the conjecture by posing sufficient conditions and constructing distance antimagic product graphs; the products under consideration are join, corona, and Cartesian.

#### Keywords

#### Full Text:

PDFDOI: http://dx.doi.org/10.5614/ejgta.2023.11.1.9

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